Analysis & PDE
- Anal. PDE
- Volume 6, Number 4 (2013), 973-991.
Long-time asymptotics for two-dimensional exterior flows with small circulation at infinity
We consider the incompressible Navier–Stokes equations in a two-dimensional exterior domain , with no-slip boundary conditions. Our initial data are of the form , where is the Oseen vortex with unit circulation at infinity and is a solenoidal perturbation belonging to for some . If is sufficiently small, we show that the solution behaves asymptotically in time like the self-similar Oseen vortex with circulation . This is a global stability result, in the sense that the perturbation can be arbitrarily large, and our smallness assumption on the circulation is independent of the domain .
Anal. PDE, Volume 6, Number 4 (2013), 973-991.
Received: 28 February 2012
Accepted: 6 August 2012
First available in Project Euclid: 20 December 2017
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Gallay, Thierry; Maekawa, Yasunori. Long-time asymptotics for two-dimensional exterior flows with small circulation at infinity. Anal. PDE 6 (2013), no. 4, 973--991. doi:10.2140/apde.2013.6.973. https://projecteuclid.org/euclid.apde/1513731386